JEE Advanced 2015 Paper 2 Offline

MCQ (More than One Correct Answer)

-1

Let $$F:R \to R$$ be a thrice differentiable function. Suppose that
$$F\left( 1 \right) = 0,F\left( 3 \right) = - 4$$ and $$F'\left( x \right) < 0$$ for all $$x \in \left( {{1 \over 2},3} \right).$$ Let $$f\left( x \right) = xF\left( x \right)$$ for all $$x \in R.$$

The correct statement(s) is (are)

$$f'\left( 1 \right) < 0$$

$$f\left( 2 \right) < 0$$

$$f'\left( x \right) \ne 0$$ for any $$x \in \left( {1,3} \right)$$

$$f'\left( x \right) = 0$$ for some $$x \in \left( {1,3} \right)$$

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